Dimension of slices through fractals with initial cubic pattern
Dimension of slices through fractals with initial cubic pattern
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DOI：
10.1007/s11401-017-1029-1
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发表时间：
2017-09
期刊：
影响因子：
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通讯作者：
Lifeng Xi;Wen Wu;Ying Xiong
中科院分区：
文献类型：
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作者：
Lifeng Xi;Wen Wu;Ying Xiong
In this paper, the Hausdorff dimension of the intersection of self-similar fractals in Euclidean space Rngenerated from an initial cube pattern with an (n−m)-dimensional hyperplaneVin a fixed direction is discussed. The authors give a sufficient condition which ensures that the Hausdorff dimensions of the slices of the fractal sets generated by “multi-rules” take the value in Marstrand’s theorem, i.e., the dimension of the self-similar sets minus one. For the self-similar fractals generated with initial cube pattern, this sufficient condition also ensures that the projection measureμVis absolutely continuous with respect to the Lebesgue measureLm. WhenμV≪Lm, the connection of the local dimension ofμVand the box dimension of slices is given.
